# Tag Archives: mathematics

May 26, 2011, 8:01 pm

As part of preparing for our impending move from Indy to Grand Rapids, my family and I have made a couple of visits to the area. These by necessity combine business with pleasure, since our three kids (ages 2, 5, and 7) don’t handle extended amounts of business well. On the last visit, we spent some time at the Grand Rapids Childrens Museum, the second floor of which is full of stuff that could occupy children — and mathematicians — for hours. This “exhibit” was, for me, one of the most evocative. Have a look:

I asked this on Twitter a few days ago, but I’ll repost it here: In the spirit of Dan Meyer’s Any Questions? meme, what questions come to mind as you watch this? Particularly math, physics, etc. questions.

One other thing — just after I wrapped up the video on this, someone put one of the little discs rolling on the turntable…

May 10, 2011, 7:42 am

# Understanding "understanding"

This past Saturday, I was grading a batch of tests that weren’t looking so great at the time, and I tweeted:

I do ask these two questions a lot in my classes, and despite what I tweeted, I will probably continue to do so. Sometimes when I do this, I get questions, and sometimes only silence. When it’s silence, I am often skeptical, but I am willing to let students have their end of the responsibility of seeking help when they need it and handling the consequences if they don’t.

But in many cases, such as with this particular test, the absence of questions leads to unresolved issues with learning, which compound themselves when a new topic is connected to the old one, compounded further when the next topic is reached, and so on. Unresolved questions are like an invasive species entering an ecosystem. Pretty soon, it becomes impossible even to ask or answer questions about the material…

February 25, 2011, 8:00 am

# Technology making a distinction but not a difference?

This article is the second one that I’ve done for Education Debate at Online Schools. It first appeared there on Tuesday this week, and now that it’s fermented a little I’m crossposting it here.

The University of South Florida‘s mathematics department has begun a pilot project to redesign its lower-level mathematics courses, like College Algebra, around a large-scale infusion of technology. This “new way of teaching college math” (to use the article’s language) involves clickers, lecture capture, software-based practice tools, and online homework systems. It’s an ambitious attempt to “teach [students] how to teach themselves”, in the words of professor and project participant Fran Hopf.

It’s a pilot project, so it remains to be seen if this approach makes a difference in improving the pass rates for students in lower-level math courses like College Algebra, which have been at around 60…

January 12, 2011, 1:41 pm

# Another thought from Papert

Image via Wikipedia

Like I said yesterday, I’m reading through Seymour Papert’s Mindstorms: Children, Computers, and Powerful Ideas right now. It is full of potent ideas about education that are reverberating in my brain as I read it. Here’s another quote from the chapter titled “Mathophobia: The Fear of Learning”:

Our children grow up in a culture permeated with the idea that there are “smart people” and “dumb people.” The social construction of the individual is as a bundle of aptitudes. There are people who are “good at math” and people who “can’t do math.” Everything is set up for children to attribute their first unsuccessful or unpleasant learning experiences to their own disabilities. As a result, children perceive failure as relegating them either to the group of “dumb people” or, more often, to a group of…

January 4, 2011, 8:41 pm

# Bound for New Orleans

Happy New Year, everyone. The blogging was light due to a nice holiday break with the family. Now we’re all back home… and I’m taking off again. This time, I’m headed to the Joint Mathematics Meetings in New Orleans from January 5 through January 8. I tend to do more with my Twitter account during conferences than I do with the blog, but hopefully I can give you some reporting along with some of the processing I usually do following good conference talks (and even some of the bad ones).

I’m giving two talks while in New Orleans:

• On Thursday at 3:55, I’m speaking on “A Brief Fly-Through of Cryptology for First-Semester Students using Active Learning and Common Technology” in the MAA Session on Cryptology for Undergraduates. That’s in the Great Ballroom E, 5th Floor Sheraton in case you’re there and want to come. This talk is about a 5-day minicourse I do as a guest lecturer in our…

December 23, 2010, 8:00 am

# Conrad Wolfram's vision for mathematics education

A partial answer to the questions I brought up in the last post about what authentic mathematics consists of, and how we get students to learn it genuinely, might be found in this TED talk by Conrad Wolfram called “Teaching kids real math with computers”. It’s 17 minutes long, but take some time to watch the whole thing:

[ted id=1007]

Profound stuff. Are we looking at the future of mathematics education in utero here?

December 22, 2010, 12:00 pm

# Misunderstanding mathematics

Image via Wikipedia

Robert Lewis, a professor at Fordham University, has published this essay entitled “Mathematics: The Most Misunderstood Subject”. The source of the general public’s misunderstandings of math, he writes, is:

…the notion that mathematics is about formulas and cranking out computations. It is the unconsciously held delusion that mathematics is a set of rules and formulas that have been worked out by God knows who for God knows why, and the student’s duty is to memorize all this stuff. Such students seem to feel that sometime in the future their boss will walk into the office and demand “Quick, what’s the quadratic formula?” Or, “Hurry, I need to know the derivative of 3x^2 – 6x +1.” There are no such employers.

Prof. Lewis goes on to describe some ways in which this central misconception is worked…

November 29, 2010, 9:00 am

# What correlates with problem solving skill?

About a year ago, I started partitioning up my Calculus tests into three sections: Concepts, Mechanics, and Problem Solving. The point values for each are 25, 25, and 50 respectively. The Concepts items are intended to be ones where no calculations are to be performed; instead students answer questions, interpret meanings of results, and draw conclusions based only on graphs, tables, or verbal descriptions. The Mechanics items are just straight-up calculations with no context, like “take the derivative of $$y = \sqrt{x^2 + 1}$$”. The Problem-Solving items are a mix of conceptual and mechanical tasks and can be either instances of things the students have seen before (e.g. optimzation or related rates problems) or some novel situation that is related to, but not identical to, the things they’ve done on homework and so on.

I did this to stress to students that the main goal of taking …

October 26, 2010, 12:00 pm

# Questions about an enVisionMATH worksheet (part 2)

Here’s another question about the same enVisionMATH worksheet we first met yesterday. Take a look at this section, and think about the mental processes you’d use to answer each of these problems:

Got it? Now, let me zoom out a little and show you a part of the worksheet you didn’t see before:

If you’re late to the party and don’t know what’s meant by “near doubles” and the arithmetic rules that enVisionMATH attaches to near doubles, read this post first. Questions:

• Now that you know that these are supposed to be exercises about near doubles, does that change the mental processes you selected earlier for working the problems?
• Should it?

October 25, 2010, 8:52 pm

# Questions about an enVisionMATH worksheet (part 1)

The 6-year old had Fall Break last week, so no homework and no enVisionMATH-blogging for me. Tonight, however, she brought home a new worksheet for her weekly homework, and a couple of things caught my eye. I thought I’d throw those out there to you all, along with a question or two, as a two-part blog post.

For the first post, take a look at this (click to enlarge):

Questions:

• In your own words, preferably those that a smart 6-year old could understand, what is the basic principle that this page is trying to get across?
• What technique does this worksheet want kids to use when doing the Algebra problems?
• What’s your opinion about the principle/technique you think the worksheet is trying to communciate? Reasonable? Natural? Likely to be useful, or used frequently later on?

• The Chronicle of Higher Education
• 1255 Twenty-Third St., N.W.
• Washington, D.C. 20037